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We investigate theoretically the $K^{0} p$ invariant mass spectrum of the$K^{+} d \to K^{0} p p$ reaction and scrutinize how the signal of the "$\Theta^{+}$" pentaquark, if it exists, emerges in the $K^{0} p$ spectrum. The mostprominent advantage of this reaction is that we can clearly judge whether the"$\Theta ^{+}$" exists or not as a direct-formation production withoutsignificant backgrounds, in contrast to other reactions such as photoproductionand $\pi$-induced productions. We show that while the impulse or single-stepscattering process can cover the "$\Theta ^{+}$" energy region with an initialkaon momentum $k_{\mathrm{lab}} \approx 0.40\, \mathrm{GeV} / c$ in thelaboratory frame, the contributions from double-step processes may have apotential possibility to reach the "$\Theta ^{+}$" energy region with a higherkaon momentum $k_{\mathrm{lab}} \sim 1 \, \mathrm{GeV} / c$. Assuming that thefull decay width of the "$\Theta ^{+}$" is around $0.5\, \mathrm{MeV}$, wepredict that the magnitude of the peak corresponding to the "$\Theta^+$" isaround a few hundred $\mu \mathrm{b}$ to $1\, \mathrm{mb}$ with the momentum ofthe kaon beam $k_{\mathrm{lab}} \approx 0.40\, \mathrm{GeV} / c$ while it isaround $\lesssim 1\, \mu \mathrm{b}$ with $k_{\mathrm{lab}} \approx 0.85\,\mathrm{GeV} / c$. Thus, the "$\Theta^+$" peak is more likely to be seen at$k_{\mathrm{lab}} \approx 0.40\, \mathrm{GeV} / c$ than at $k_{\mathrm{lab}}\approx 0.85 \,\mathrm{GeV} / c$.

Feasibility study of the $K^{+} d \to K^{0} p p$ reaction for the "$\Theta ^{+}$" pentaquark